Posts Tagged: manifesto

Jul 13

Morality needs probability, manifesto addendum

Just added to my Big Bright Green Manifesto Machine. You might need to read this through a couple times; it’s a difficult concept since it lives in a collective blind spot for us:

Doing ethics without probability is like performing surgery with a wooden spoon — it’s a blunt instrument capable of only the most basic operations, and more likely to kill the patient than heal them. Implicitly, we understand this need for probability in making ethical judgements, yet most people recoil when the calculus of probabilities is made explicit, because it seems cold, because the math frightens and confuses them, or because letting odds remain unestimated and unacknowledged allows people to confuse positive outcomes with moral behavior, sweeping hidden risks under the rug when things go well, or claiming ignorance when they don’t. It’s time to acknowledge — directly, explicitly, mathematically — that morality needs probability. For ethics to move forward it must be integrated with our knowledge of randomness and partial entailment.

Here’s an example of how we already take probability into account implicitly. If we retrieve our lost ball from someone’s yard without asking first, we justify this based on our belief that the owner is more likely to be bothered by us interrupting their dinner, than by our temporary trespass on their lawn. The greater the probability of great harm, the higher the level of certainty we demand. Our most heated debates involve situations where the probability of harm from both action and inaction is high. If someone’s dog is stuck in a hot car on a sunny day, should you break in and try to save it? Does the chance of a dog dying of heatstroke justify a forced entry that will probably result in expensive damage and an irate owner (though it’s possible they would be grateful instead). If you decide to break in, how long should you wait first? What prior distribution should you put on the owner’s return time, and how do you update your prior as time goes by? If the waiting time is chi-square on low degrees of freedom, your concern for the dog might be unjustified. If it follows the unreliable friend distribution, you may be that dog’s only hope.

As I hope is becoming clear, questions of morality cannot be resolved without asking questions about probability. If the example above seems trivial (perhaps the owner’s property rights trump your concern for a dog), then substitute the animal for a toddler who looks uncomfortably warm. Now how long do you wait, and how do you deal with the risk that smashing a window might harm the child?

Apr 13

Manifesto addition: “N is always finite”

Added one more point to my manifesto:

“N” is always finite. Probability theory gives us many powerful limit theorems. These tell us what to expect, mathematically, as the number of trials goes to infinity. That fine, but we don’t live our lives at the limit. In the real world, asymptotics are much more important, as are non-parametric inference and tools like bootstrap to maximize the information extracted from small sample sizes. Even in those real life situations when N could increase without limit, the growth of the sample size itself can change the problem. Toss a die enough times and the edges will start to wear off, changing the frequency that each side comes up.

Had to add it after reading the phrase “if we let N go to infinity” one to many times.

May 12

May Manifesto addendum

Just added another statement to my manifesto. Here is the full text:

Interpret or predict. Pick one. There is an inescapable tradeoff between models which are easy to interpret and those which make the best predictions. The larger the data set, the higher the dimensions, the more interpretability needs to be sacrificed to optimize prediction quality. This puts modern science at a crossroads, having now exploited all the low hanging fruit of simple models of the natural world. In order to move forward, we will have to put ever more confidence in complex, uninterpretable “black box” algorithms, based solely on their power to reliably predict new observations.

Since you can’t comment to WordPress pages, you can post any comments about my latest addition here. First, though, here is an example that might help explain the difference between interpreting and predicting. Suppose you wanted to say something about smoking and its effect on health. If your focus is on interpretability, you might create a simple model (perhaps using a hazards ratio) that leads you to make the following statement: “Smoking increases your risk of developing lounge cancer by 100%”.

There may be some broad truth to your statement, but to more effectively predicts whether a particular individual will develop cancer, you’ll need to include dozens of additional factors in your model. A simple proportional hazards model might be outperformed by an exotic form of regression, which might be outperformed by a neural network, which would probably be outperformed by an ensemble of various methods. At which point, you can no longer claim that smoking makes people twice as likely to get cancer. Instead, you could say that if Mrs. Jones —a real estate agent and mother of two, in her early 30s, with no family history of cancer — begins smoking two packs a day of filtered cigarettes, your model predicts that she will be 70% more likely to be diagnosed with lounge cancer in the next 10 years.

The shift taking place right now in how we do science is huge, so big that we’ve barely noticed. Instead of seeing the world as a set of discrete, causal linkages, this new approach sees rich webs of interconnections, correlations and feedback loops. In order to gain real traction in simulating (and making predictions about) complex systems in biology, economics and ecology, we’ll need to give up on the ideal of understanding them.

Nov 11

Manifesto update

I just got done tweaking some of the points in my Manifesto and added a new one about evidence. As before, the Manifesto is a work in progress; your feedback is welcome here since you can’t post comments to pages in WordPress.